A college football coach wants to know if there is a correlation between his players' leg strength and the speed at which they can sprint 40 yards. He sets up the following test and records the data:

Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he as each player sprint 40 yards every day. The table shows the average number of leg-press repetitions and the average 40-yard- dash time (in seconds) for 7 randomly selected players. What is the equation of the line of best fit? How fast could he expect a player to run 40 yards if that player can reach 22 leg-press repetitions? Round any value to the nearest tenth, if possible.

Leg Press: 15, 18, 8, 30, 26, 12, 21
40-yard Dash: 5.2, 6.3, 6.8, 8.2, 8.0, 5.3, 5.9

My answer:

6.89, however when rounded it'd go to 6.9

you'd use IP divided by PL which would equal SP/Distance equal player

am I correct?

Ack

To find the equation of the line of best fit, you need to perform a linear regression analysis on the given data. This will help determine the relationship between the number of leg press repetitions and the 40-yard dash time.

Linear regression finds the equation of a line that best represents the relationship between two variables. In this case, the independent variable (x) is the number of leg press repetitions, and the dependent variable (y) is the 40-yard dash time.

First, let's calculate the means of both variables:
Mean of leg press repetitions (x):
(15 + 18 + 8 + 30 + 26 + 12 + 21) / 7 = 21.9

Mean of 40-yard dash times (y):
(5.2 + 6.3 + 6.8 + 8.2 + 8.0 + 5.3 + 5.9) / 7 = 6.5

Next, calculate the deviations from the mean for both variables:
Deviation of leg press repetitions (x):
15 - 21.9 = -6.9
18 - 21.9 = -3.9
8 - 21.9 = -13.9
30 - 21.9 = 8.1
26 - 21.9 = 4.1
12 - 21.9 = -9.9
21 - 21.9 = -0.9

Deviation of 40-yard dash times (y):
5.2 - 6.5 = -1.3
6.3 - 6.5 = -0.2
6.8 - 6.5 = 0.3
8.2 - 6.5 = 1.7
8.0 - 6.5 = 1.5
5.3 - 6.5 = -1.2
5.9 - 6.5 = -0.6

To find the slope of the line, calculate the sum of the products of the deviations:
Sum of (deviation of x * deviation of y):
-6.9 * -1.3 + (-3.9) * (-0.2) + (-13.9) * 0.3 + 8.1 * 1.7 + 4.1 * 1.5 + (-9.9) * (-1.2) + (-0.9) * (-0.6) = 77.37

Next, calculate the sum of the squared deviations of x:
Sum of (deviation of x)^2:
(-6.9)^2 + (-3.9)^2 + (-13.9)^2 + 8.1^2 + 4.1^2 + (-9.9)^2 + (-0.9)^2 = 680.37

Now, calculate the slope (m) of the line:
m = (sum of (deviation of x * deviation of y)) / (sum of (deviation of x)^2)
m = 77.37 / 680.37 ≈ 0.1137

Finally, find the y-intercept (b) of the line:
b = mean of y - (m * mean of x)
b = 6.5 - (0.1137 * 21.9) ≈ 3.16

Therefore, the equation of the line of best fit is:
y = 0.1137x + 3.16

To predict how fast a player could run 40 yards if they can achieve 22 leg press repetitions, substitute x = 22 into the equation:
y = 0.1137 * 22 + 3.16 ≈ 5.08

Therefore, the player could be expected to run approximately 5.1 seconds for the 40-yard dash if they can reach 22 leg press repetitions.